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      <h1 class="site-logo" id="site-title">深入浅出PyTorch</h1>
      
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  <a class="reference internal" href="../%E7%AC%AC%E4%B8%80%E7%AB%A0/index.html">
   第一章：PyTorch的简介和安装
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     1.1 PyTorch简介
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     1.2 PyTorch的安装
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     1.3 PyTorch相关资源
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   第二章：PyTorch基础知识
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     2.1 张量
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     2.2 自动求导
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     2.3 并行计算简介
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   第三章：PyTorch的主要组成模块
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     3.1 思考：完成深度学习的必要部分
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     3.2 基本配置
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     3.3 数据读入
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     3.4 模型构建
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     3.5 模型初始化
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     3.6 损失函数
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     3.7 训练和评估
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     3.8 可视化
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     3.9 Pytorch优化器
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   第四章：PyTorch基础实战
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     基础实战——FashionMNIST时装分类
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   第五章：PyTorch模型定义
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     5.1 PyTorch模型定义的方式
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    <a class="reference internal" href="../%E7%AC%AC%E4%BA%94%E7%AB%A0/5.2%20%E5%88%A9%E7%94%A8%E6%A8%A1%E5%9E%8B%E5%9D%97%E5%BF%AB%E9%80%9F%E6%90%AD%E5%BB%BA%E5%A4%8D%E6%9D%82%E7%BD%91%E7%BB%9C.html">
     5.2 利用模型块快速搭建复杂网络
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    <a class="reference internal" href="../%E7%AC%AC%E4%BA%94%E7%AB%A0/5.3%20PyTorch%E4%BF%AE%E6%94%B9%E6%A8%A1%E5%9E%8B.html">
     5.3 PyTorch修改模型
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    <a class="reference internal" href="../%E7%AC%AC%E4%BA%94%E7%AB%A0/5.4%20PyTorh%E6%A8%A1%E5%9E%8B%E4%BF%9D%E5%AD%98%E4%B8%8E%E8%AF%BB%E5%8F%96.html">
     5.4 PyTorch模型保存与读取
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   第六章：PyTorch进阶训练技巧
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     6.1 自定义损失函数
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     6.2 动态调整学习率
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     6.3 模型微调-torchvision
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     6.3 模型微调 - timm
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    <a class="reference internal" href="../%E7%AC%AC%E5%85%AD%E7%AB%A0/6.4%20%E5%8D%8A%E7%B2%BE%E5%BA%A6%E8%AE%AD%E7%BB%83.html">
     6.4 半精度训练
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    <a class="reference internal" href="../%E7%AC%AC%E5%85%AD%E7%AB%A0/6.5%20%E6%95%B0%E6%8D%AE%E5%A2%9E%E5%BC%BA-imgaug.html">
     6.5 数据增强-imgaug
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    <a class="reference internal" href="../%E7%AC%AC%E5%85%AD%E7%AB%A0/6.6%20%E4%BD%BF%E7%94%A8argparse%E8%BF%9B%E8%A1%8C%E8%B0%83%E5%8F%82.html">
     6.6 使用argparse进行调参
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    <a class="reference internal" href="../%E7%AC%AC%E5%85%AD%E7%AB%A0/PyTorch%E6%A8%A1%E5%9E%8B%E5%AE%9A%E4%B9%89%E4%B8%8E%E8%BF%9B%E9%98%B6%E8%AE%AD%E7%BB%83%E6%8A%80%E5%B7%A7.html">
     PyTorch模型定义与进阶训练技巧
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   第七章：PyTorch可视化
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     7.1 可视化网络结构
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    <a class="reference internal" href="../%E7%AC%AC%E4%B8%83%E7%AB%A0/7.2%20CNN%E5%8D%B7%E7%A7%AF%E5%B1%82%E5%8F%AF%E8%A7%86%E5%8C%96.html">
     7.2 CNN可视化
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    <a class="reference internal" href="../%E7%AC%AC%E4%B8%83%E7%AB%A0/7.3%20%E4%BD%BF%E7%94%A8TensorBoard%E5%8F%AF%E8%A7%86%E5%8C%96%E8%AE%AD%E7%BB%83%E8%BF%87%E7%A8%8B.html">
     7.3 使用TensorBoard可视化训练过程
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   第八章：PyTorch生态简介
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     8.1 本章简介
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     8.2 torchvision
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     8.3 PyTorchVideo简介
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     8.4 torchtext简介
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     transforms实战
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                <h1>2.2 自动求导</h1>
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  <section class="tex2jax_ignore mathjax_ignore" id="id1">
<h1>2.2 自动求导<a class="headerlink" href="#id1" title="永久链接至标题">#</a></h1>
<p>PyTorch 中，所有神经网络的核心是 <code class="docutils literal notranslate"><span class="pre">autograd</span> </code>包。autograd包为张量上的所有操作提供了自动求导机制。它是一个在运行时定义 ( define-by-run ）的框架，这意味着反向传播是根据代码如何运行来决定的，并且每次迭代可以是不同的。</p>
<p><code class="docutils literal notranslate"><span class="pre">torch.Tensor</span> </code>是这个包的核心类。如果设置它的属性<code class="docutils literal notranslate"> <span class="pre">.requires_grad</span></code> 为 <code class="docutils literal notranslate"><span class="pre">True</span></code>，那么它将会追踪对于该张量的所有操作。当完成计算后可以通过调用<code class="docutils literal notranslate"> <span class="pre">.backward()</span></code>，来自动计算所有的梯度。这个张量的所有梯度将会自动累加到<code class="docutils literal notranslate"><span class="pre">.grad</span></code>属性。</p>
<p>注意：在 y.backward() 时，如果 y 是标量，则不需要为 backward() 传入任何参数；否则，需要传入一个与 y 同形的Tensor。</p>
<p>要阻止一个张量被跟踪历史，可以调用<code class="docutils literal notranslate"><span class="pre">.detach()</span></code>方法将其与计算历史分离，并阻止它未来的计算记录被跟踪。为了防止跟踪历史记录(和使用内存），可以将代码块包装在 <code class="docutils literal notranslate"><span class="pre">with</span> <span class="pre">torch.no_grad():</span> </code>中。在评估模型时特别有用，因为模型可能具有 <code class="docutils literal notranslate"><span class="pre">requires_grad</span> <span class="pre">=</span> <span class="pre">True</span></code> 的可训练的参数，但是我们不需要在此过程中对他们进行梯度计算。</p>
<p>还有一个类对于<code class="docutils literal notranslate"><span class="pre">autograd</span></code>的实现非常重要：<code class="docutils literal notranslate"><span class="pre">Function</span></code>。<code class="docutils literal notranslate"><span class="pre">Tensor</span> </code>和<code class="docutils literal notranslate"> <span class="pre">Function</span></code> 互相连接生成了一个无环图 (acyclic graph)，它编码了完整的计算历史。每个张量都有一个<code class="docutils literal notranslate"><span class="pre">.grad_fn</span></code>属性，该属性引用了创建 <code class="docutils literal notranslate"><span class="pre">Tensor</span> </code>自身的<code class="docutils literal notranslate"><span class="pre">Function</span></code>(除非这个张量是用户手动创建的，即这个张量的<code class="docutils literal notranslate"><span class="pre">grad_fn</span></code>是 <code class="docutils literal notranslate"><span class="pre">None</span></code> )。下面给出的例子中，张量由用户手动创建，因此grad_fn返回结果是None。</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">print_function</span>
<span class="kn">import</span> <span class="nn">torch</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="n">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">grad_fn</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kc">None</span>
</pre></div>
</div>
<p>如果需要计算导数，可以在 <code class="docutils literal notranslate"><span class="pre">Tensor</span></code> 上调用 <code class="docutils literal notranslate"><span class="pre">.backward()</span></code>。如果<code class="docutils literal notranslate"> <span class="pre">Tensor</span></code> 是一个标量(即它包含一个元素的数据），则不需要为 <code class="docutils literal notranslate"><span class="pre">backward()</span> </code>指定任何参数，但是如果它有更多的元素，则需要指定一个<code class="docutils literal notranslate"><span class="pre">gradient</span></code>参数，该参数是形状匹配的张量。</p>
<p>创建一个张量并设置<code class="docutils literal notranslate"><span class="pre">requires_grad=True</span></code>用来追踪其计算历史</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">x</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">tensor</span><span class="p">([[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">],</span>
        <span class="p">[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">]],</span> <span class="n">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
</pre></div>
</div>
<p>对这个张量做一次运算：</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">y</span> <span class="o">=</span> <span class="n">x</span><span class="o">**</span><span class="mi">2</span>
<span class="nb">print</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">tensor</span><span class="p">([[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">],</span>
        <span class="p">[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">]],</span> <span class="n">grad_fn</span><span class="o">=&lt;</span><span class="n">PowBackward0</span><span class="o">&gt;</span><span class="p">)</span>
</pre></div>
</div>
<p><code class="docutils literal notranslate"><span class="pre">y</span></code>是计算的结果，所以它有<code class="docutils literal notranslate"><span class="pre">grad_fn</span></code>属性。</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="n">y</span><span class="o">.</span><span class="n">grad_fn</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="o">&lt;</span><span class="n">PowBackward0</span> <span class="nb">object</span> <span class="n">at</span> <span class="mh">0x000001CB45988C70</span><span class="o">&gt;</span>
</pre></div>
</div>
<p>对 y 进行更多操作</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">z</span> <span class="o">=</span> <span class="n">y</span> <span class="o">*</span> <span class="n">y</span> <span class="o">*</span> <span class="mi">3</span>
<span class="n">out</span> <span class="o">=</span> <span class="n">z</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span>

<span class="nb">print</span><span class="p">(</span><span class="n">z</span><span class="p">,</span> <span class="n">out</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">tensor</span><span class="p">([[</span><span class="mf">3.</span><span class="p">,</span> <span class="mf">3.</span><span class="p">],</span>
        <span class="p">[</span><span class="mf">3.</span><span class="p">,</span> <span class="mf">3.</span><span class="p">]],</span> <span class="n">grad_fn</span><span class="o">=&lt;</span><span class="n">MulBackward0</span><span class="o">&gt;</span><span class="p">)</span> <span class="n">tensor</span><span class="p">(</span><span class="mf">3.</span><span class="p">,</span> <span class="n">grad_fn</span><span class="o">=&lt;</span><span class="n">MeanBackward0</span><span class="o">&gt;</span><span class="p">)</span>
</pre></div>
</div>
<p><code class="docutils literal notranslate"><span class="pre">.requires_grad_(...)</span> </code>原地改变了现有张量的<code class="docutils literal notranslate"><span class="pre">requires_grad</span></code>标志。如果没有指定的话，默认输入的这个标志是<code class="docutils literal notranslate"> <span class="pre">False</span></code>。</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span> <span class="c1"># 缺失情况下默认 requires_grad = False</span>
<span class="n">a</span> <span class="o">=</span> <span class="p">((</span><span class="n">a</span> <span class="o">*</span> <span class="mi">3</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">a</span> <span class="o">-</span> <span class="mi">1</span><span class="p">))</span>
<span class="nb">print</span><span class="p">(</span><span class="n">a</span><span class="o">.</span><span class="n">requires_grad</span><span class="p">)</span>
<span class="n">a</span><span class="o">.</span><span class="n">requires_grad_</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">a</span><span class="o">.</span><span class="n">requires_grad</span><span class="p">)</span>
<span class="n">b</span> <span class="o">=</span> <span class="p">(</span><span class="n">a</span> <span class="o">*</span> <span class="n">a</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="n">b</span><span class="o">.</span><span class="n">grad_fn</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kc">False</span>
<span class="kc">True</span>
<span class="o">&lt;</span><span class="n">SumBackward0</span> <span class="nb">object</span> <span class="n">at</span> <span class="mh">0x000001CB4A19FB50</span><span class="o">&gt;</span>
</pre></div>
</div>
<p><strong>梯度</strong></p>
<p>现在开始进行反向传播，因为<code class="docutils literal notranslate"> <span class="pre">out</span></code> 是一个标量，因此<code class="docutils literal notranslate"><span class="pre">out.backward()</span></code>和<code class="docutils literal notranslate"> <span class="pre">out.backward(torch.tensor(1.))</span></code> 等价。</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">out</span><span class="o">.</span><span class="n">backward</span><span class="p">()</span>
</pre></div>
</div>
<p>输出导数<code class="docutils literal notranslate"> <span class="pre">d(out)/dx</span></code></p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">grad</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">tensor</span><span class="p">([[</span><span class="mf">3.</span><span class="p">,</span> <span class="mf">3.</span><span class="p">],</span>
        <span class="p">[</span><span class="mf">3.</span><span class="p">,</span> <span class="mf">3.</span><span class="p">]])</span>
</pre></div>
</div>
<p>数学上，若有向量函数<span class="math notranslate nohighlight">\(\vec{y}=f(\vec{x})\)</span>，那么 <span class="math notranslate nohighlight">\(\vec{y}\)</span> 关于 <span class="math notranslate nohighlight">\(\vec{x}\)</span> 的梯度就是一个雅可比矩阵：
<span class="math notranslate nohighlight">\(
J=\left(\begin{array}{ccc}\frac{\partial y_{1}}{\partial x_{1}} &amp; \cdots &amp; \frac{\partial y_{1}}{\partial x_{n}} \\ \vdots &amp; \ddots &amp; \vdots \\ \frac{\partial y_{m}}{\partial x_{1}} &amp; \cdots &amp; \frac{\partial y_{m}}{\partial x_{n}}\end{array}\right)
\)</span>
而 <code class="docutils literal notranslate"><span class="pre">torch.autograd</span></code> 这个包就是用来计算一些雅可比矩阵的乘积的。例如，如果 <span class="math notranslate nohighlight">\(v\)</span> 是一个标量函数 <span class="math notranslate nohighlight">\(l = g(\vec{y})\)</span> 的梯度：
<span class="math notranslate nohighlight">\(
v=\left(\begin{array}{lll}\frac{\partial l}{\partial y_{1}} &amp; \cdots &amp; \frac{\partial l}{\partial y_{m}}\end{array}\right)
\)</span>
由链式法则，我们可以得到：
<span class="math notranslate nohighlight">\(
v J=\left(\begin{array}{lll}\frac{\partial l}{\partial y_{1}} &amp; \cdots &amp; \frac{\partial l}{\partial y_{m}}\end{array}\right)\left(\begin{array}{ccc}\frac{\partial y_{1}}{\partial x_{1}} &amp; \cdots &amp; \frac{\partial y_{1}}{\partial x_{n}} \\ \vdots &amp; \ddots &amp; \vdots \\ \frac{\partial y_{m}}{\partial x_{1}} &amp; \cdots &amp; \frac{\partial y_{m}}{\partial x_{n}}\end{array}\right)=\left(\begin{array}{lll}\frac{\partial l}{\partial x_{1}} &amp; \cdots &amp; \frac{\partial l}{\partial x_{n}}\end{array}\right)
\)</span></p>
<p>注意：grad在反向传播过程中是累加的(accumulated)，这意味着每一次运行反向传播，梯度都会累加之前的梯度，所以一般在反向传播之前需把梯度清零。</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># 再来反向传播⼀一次，注意grad是累加的</span>
<span class="n">out2</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
<span class="n">out2</span><span class="o">.</span><span class="n">backward</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">grad</span><span class="p">)</span>

<span class="n">out3</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
<span class="n">x</span><span class="o">.</span><span class="n">grad</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">zero_</span><span class="p">()</span>
<span class="n">out3</span><span class="o">.</span><span class="n">backward</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">grad</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">tensor</span><span class="p">([[</span><span class="mf">4.</span><span class="p">,</span> <span class="mf">4.</span><span class="p">],</span>
        <span class="p">[</span><span class="mf">4.</span><span class="p">,</span> <span class="mf">4.</span><span class="p">]])</span>
<span class="n">tensor</span><span class="p">([[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">],</span>
        <span class="p">[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">]])</span>
</pre></div>
</div>
<p>现在我们来看一个雅可比向量积的例子：</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">x</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>

<span class="n">y</span> <span class="o">=</span> <span class="n">x</span> <span class="o">*</span> <span class="mi">2</span>
<span class="n">i</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">while</span> <span class="n">y</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">norm</span><span class="p">()</span> <span class="o">&lt;</span> <span class="mi">1000</span><span class="p">:</span>
    <span class="n">y</span> <span class="o">=</span> <span class="n">y</span> <span class="o">*</span> <span class="mi">2</span>
    <span class="n">i</span> <span class="o">=</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span>
<span class="nb">print</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">tensor</span><span class="p">([</span><span class="o">-</span><span class="mf">0.9332</span><span class="p">,</span>  <span class="mf">1.9616</span><span class="p">,</span>  <span class="mf">0.1739</span><span class="p">],</span> <span class="n">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">tensor</span><span class="p">([</span><span class="o">-</span><span class="mf">477.7843</span><span class="p">,</span> <span class="mf">1004.3264</span><span class="p">,</span>   <span class="mf">89.0424</span><span class="p">],</span> <span class="n">grad_fn</span><span class="o">=&lt;</span><span class="n">MulBackward0</span><span class="o">&gt;</span><span class="p">)</span>
<span class="mi">8</span>
</pre></div>
</div>
<p>在这种情况下，<code class="docutils literal notranslate"><span class="pre">y</span> </code>不再是标量。<code class="docutils literal notranslate"><span class="pre">torch.autograd</span></code> 不能直接计算完整的雅可比矩阵，但是如果我们只想要雅可比向量积，只需将这个向量作为参数传给 <code class="docutils literal notranslate"><span class="pre">backward：</span></code></p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">v</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">tensor</span><span class="p">([</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0001</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">float</span><span class="p">)</span>
<span class="n">y</span><span class="o">.</span><span class="n">backward</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>

<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">grad</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">tensor</span><span class="p">([</span><span class="mf">5.1200e+01</span><span class="p">,</span> <span class="mf">5.1200e+02</span><span class="p">,</span> <span class="mf">5.1200e-02</span><span class="p">])</span>
</pre></div>
</div>
<p>也可以通过将代码块包装在<code class="docutils literal notranslate"> <span class="pre">with</span> <span class="pre">torch.no_grad():</span></code> 中，来阻止 autograd 跟踪设置了<code class="docutils literal notranslate"><span class="pre">.requires_grad=True</span></code>的张量的历史记录。</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">requires_grad</span><span class="p">)</span>
<span class="nb">print</span><span class="p">((</span><span class="n">x</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">requires_grad</span><span class="p">)</span>

<span class="k">with</span> <span class="n">torch</span><span class="o">.</span><span class="n">no_grad</span><span class="p">():</span>
    <span class="nb">print</span><span class="p">((</span><span class="n">x</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">requires_grad</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kc">True</span>
<span class="kc">True</span>
<span class="kc">False</span>
</pre></div>
</div>
<p>如果我们想要修改 tensor 的数值，但是又不希望被 autograd 记录(即不会影响反向传播)， 那么我们可以对 tensor.data 进行操作。</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">x</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>

<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">data</span><span class="p">)</span> <span class="c1"># 还是一个tensor</span>
<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">requires_grad</span><span class="p">)</span> <span class="c1"># 但是已经是独立于计算图之外</span>

<span class="n">y</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">x</span>
<span class="n">x</span><span class="o">.</span><span class="n">data</span> <span class="o">*=</span> <span class="mi">100</span> <span class="c1"># 只改变了值，不会记录在计算图，所以不会影响梯度传播</span>

<span class="n">y</span><span class="o">.</span><span class="n">backward</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="c1"># 更改data的值也会影响tensor的值 </span>
<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">grad</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">tensor</span><span class="p">([</span><span class="mf">1.</span><span class="p">])</span>
<span class="kc">False</span>
<span class="n">tensor</span><span class="p">([</span><span class="mf">100.</span><span class="p">],</span> <span class="n">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">tensor</span><span class="p">([</span><span class="mf">2.</span><span class="p">])</span>
</pre></div>
</div>
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